Elastic interaction of spherical nanoinhomogeneities with Gurtin–Murdoch type interfaces

Кущ, В. І.; Mogilevskaya, Sofia G.; Stolarski, Henryk K.; Crouch, Steven L.

doi:10.1016/j.jmps.2011.06.004

Cited by 72 publications

(30 citation statements)

References 26 publications

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“…The above equation obviously represents a jump of 2τ 0 /a across the interface, as dictated by the first part of equation (17). As seen from Figure 2, the impact of the half-space surface on the modified solution shows similar characteristics to those of the classical solution.…”

Section: Resultsmentioning

confidence: 78%

“…All contributions should be included in its derivation, both elastic and nonelastic. In particular, the contribution due to the eigenstrain load, equation (12), plays its role through the interface constitutive relationship, equation (15), and the evaluation formulae of the interface divergence, equation (17). For brevity, the explicit expressions of displacements, stresses, and interface divergence of interface displacements have been omitted.…”

Section: Methods Of Solutionmentioning

confidence: 99%

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Elastic disturbance due to a nanoparticle near a free surface

Kouris

2013

Mathematics and Mechanics of Solids

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The presence of nanoparticles in an elastic solid introduces disturbances that can vary significantly from the ones predicted by classical elasticity. In this study, we were able to determine that nanoscale effects introduced via a coherent interface model can indeed result in complex, non-local displacement and stress fields near the free surface of a substrate. The specific geometry is defined by a spherical nanoparticle near a straight boundary. The system is loaded either through a far-field uniaxial tension or a transformation strain (eigenstrain) in the particle itself. The elastic field can be fully determined using a three-dimensional displacement formulation that incorporates a well-established interface model.

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Section: Resultsmentioning

confidence: 78%

Section: Methods Of Solutionmentioning

confidence: 99%

Elastic disturbance due to a nanoparticle near a free surface

Kouris

2013

Mathematics and Mechanics of Solids

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“…(b) Interface equilibrium conditions (on the kth interface in terms of the normal and tangential ð3 0 ; 2 0 ; 1 0 Þ-components of the interface in which 3 0 denotes the normal direction, 2 0 and 1 0 represent the tangential directions g and n, respectively) from the vector forms (Mogilevskaya et al, 2008;Kushch et al, 2011) can be written as the corresponding component forms as follows…”

Section: Basic Formulationmentioning

confidence: 99%

“…As an alternative to the DBEM, the SBEM developed by Dong (2012) have also been used to investigate two and three dimensional nanoinhomogeneities. In this paper, 3D boundary integral formulation and component form of Gurtin-Murdoch constitutive relations for nanoinhomogeneities have been used based on the research of Mogilevskaya et al (2008) and Kushch et al (2011). In order to extend the mentioned work, this paper will use the sub-domain boundary element method (DBEM) and the proposed boundary integral formulation (SBEM) to further study the elastic mechanical behaviors of 3D nanoscale inhomogeneities.…”

Section: Introductionmentioning

confidence: 99%

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Boundary element analysis of three dimensional nanoscale inhomogeneities

Dong¹,

Zhang²

2013

International Journal of Solids and Structures

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a b s t r a c tThis work contains two parts, i.e. (1) the subdomain boundary element method (DBEM) and the Gurtin-Murdoch interface constitutive relation are used to investigate three dimensional (3D) nanoinhomogeneities; (2) under the condition of the same Poisson's ratio for the inhomogeneities and the matrix, an integral equation formulation only containing the interface displacements, i.e. no interface tractions, is proposed to carry out the stress analysis of 3D nano-inhomogeneities. The proposed integral equation formulation (called as SBEM) can simply be implemented in the analysis of 3D nano-inhomogeneities compared to the DBEM. This paper presents the component form of 3D Gurtin-Murdoch interface constitutive relation which can easily be used in the numerical implementation. Nine-node quadrilateral elements are adopted to discretize the interfaces among the matrix and nano-inhomogeneities. The results from two kinds of methods, i.e. DBEM and SBEM, are in good agreement with each other.

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Dynamic fracture behavior of a nanocrack in a piezoelectric plane

Rangelov

Dineva

2017

Z Angew Math Mech

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Key words Piezoelectricity, blunt nano crack, time-harmonic plane wave, BIEM, SCF. MSC (2000) 35Q74, 74S15, 74H35Scattering of time harmonic plane waves by a finite blunt nano-crack in a homogeneous transversely isotropic piezoelectric plane under plane strain conditions is studied. The mechanical model combines: (a) classical elastodynamic theory for the bulk piezoelectric solid, where the total wave comprises both incident and scattered wave field; (b) non-classical boundary conditions and localized constitutive equation for the interface between the crack and piezoelectric matrix within the frame of the Gurtin-Murdoch surface elasticity theory. The computational approach uses a non-hypersingular traction based boundary integral equation method (BIEM) basing on the fundamental solution derived in closed form by Radon transforms. Furthermore, the parametric study is presented which demonstrates the sensitivity of the generalized stress concentration fields near the crack-tip to the key parameters as the size of the crack, surface properties, coupled nature of the piezoelectricity phenomenon, type and properties of the incident wave such as frequency, wave length and wave propagation direction, dynamic interaction between the crack, incident wave and coupled electro-elastic continuum.where u * QK is a fundamental solution of Eq. (4) and σ * iJ K = C iJ Ql u * QK,l is its corresponding stress, u M J = u sc J + u in J , t in J + t sc J = t M J , and γ RJ is the jump term depending on the local geometry at the source point x. After the standard discretization and collocation procedure applied to Eq. (8) and satisfaction of the non-classical boundary condition (7), the resulting solution takes into consideration the effects of surface elasticity via the Gurtin -

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Elastic interaction of spherical nanoinhomogeneities with Gurtin–Murdoch type interfaces

Cited by 72 publications

References 26 publications

Elastic disturbance due to a nanoparticle near a free surface

Elastic disturbance due to a nanoparticle near a free surface

Boundary element analysis of three dimensional nanoscale inhomogeneities

Dynamic fracture behavior of a nanocrack in a piezoelectric plane

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